Buffering Octahedra in Mo 4 Zr 9 P: Intergrowth as a Solution to the Frustrated Packing of Tricapped Trigonal Prisms and Icosahedra.

Atomic packings based on icosahedra and tricapped trigonal prisms are prone to frustration─indeed, these polyhedra represent common configurations in metallic glasses. In this Article, we illustrate how these packing issues can serve as a driving force for the formation of modular intermetallic structures. Using Density Functional Theory-Chemical Pressure (DFT-CP) analysis, we relate the Hf 9 Mo 4 B-type structure of Mo 4 Zr 9 P to interatomic pressures experienced by the atoms in two parent structures: Zr 3 P, whose structure is built from tricapped trigonal prisms, and ZrMo 2 , a Laves phase containing icosahedra. CP analysis of Zr 3 P reveals that it has particularly frustrated packing because of the entangling of its tricapped trigonal prisms. In the ternary phase, the frustration is significantly relieved as the units become isolated from each other. Further analysis points to the stabilizing effect of a face-sharing network of octahedra in Mo 4 Zr 9 P that largely separates the structure into Zr-Mo and Zr-P domains and serves as a buffering region for the relaxation of interatomic distances. These conclusions are generalized to the broader members of this structure type with the examination of the CP schemes for the isostructural Mo 4 Zr 9 B, Al 5 Co 2 , and Mg 5 Pd 2 phases. Finally, we screen the structural literature using the ToposPro software to identify three additional structure types that have similar intergrowth patterns: the Dy 4 CoCd, La 23 Ni 7 Mg 4 , and Gd 14 Co 3 In 3 types. An analysis of the interatomic distances within the octahedral networks of these structures suggests that these networks commonly facilitate the reconciliation of packing incompatibilities in intermetallic chemistry.